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Title of Journal: Positivity

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Abbravation: Positivity

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Birkhäuser-Verlag

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DOI

10.1016/j.ajodo.2011.05.011

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1572-9281

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Regular orbits and positive directions

Authors: María del Pilar Romero de la Rosa
Publish Date: 2009/02/06
Volume: 13, Issue: 4, Pages: 631-642
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Abstract

Let A be a bounded linear operator defined on a separable Banach space X Then A is said to be supercyclic if there exists a vector x ∈ X later called supercyclic for A such that the projective orbit lambda An xn in mathbbNlambda in mathbbC is dense in X On the other hand A is said to be positive supercyclic if for each supercyclic vector x the positive projective orbit rAnx r in mathbbR +n in mathbbN is dense in X Sometimes supercyclicity and positive supercyclicity are equivalent The study of this relationship was initiated in 14 by F León and V Müller In this paper we study positive supercyclicity for operators A of the form A=T oplus alpha 1 mathbbC with alpha in mathbbCsetminus0 defined on X oplus mathbbC We will see that such a problem is related with the study of regular orbits The notion of positive directions will be central throughout the paper

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Other Papers In This Journal:
  1. Order-unit-metric spaces
  2. The Radon–Nikodym Property for Tensor Products of Banach Lattices
  3. Odd Degree Polynomials on Real Banach Spaces
  4. Positive bases in spaces of polynomials
  5. Semicontinuity of the solution set to a parametric generalized strong vector equilibrium problem
  6. A new application of non-increasing sequences
  7. On the lower semicontinuity of the solution mappings to a parametric generalized strong vector equilibrium problem
  8. A class of $$\ell ^p$$ saturated Banach spaces
  9. On the Structure of the Completion of a Normed Lattice
  10. Domination by ergodic elements in ordered Banach algebras
  11. Pentadiagonal Oscillatory Matrices with Two Spectrum in Common
  12. The essential spectral radius of Volterra operators and an application to Volterra-Hammerstein functional inclusions
  13. An iterative algorithm for finding a common solution of fixed points and a general system of variational inequalities for two inverse strongly accretive operators
  14. Perturbation of Transition Functions and a Feynman-Kac Formula for the Incorporation of Mortality
  15. Statistical approximation by double sequences of positive linear operators on modular spaces
  16. Modules and extremal completely positive maps
  17. Positive solutions of semi-positone nonlinear operator equations in Banach spaces with lattice structure
  18. A characterization of positively decomposable non-linear maps between Banach lattices
  19. Positive solutions for fractional differential systems with nonlocal Riemann–Liouville fractional integral boundary conditions
  20. Coupled coincidence point results on generalized distance in ordered cone metric spaces
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